Monday, May 28, 2012

In speculating who will be the Treasury secretary if Mitt Romney wins the presidency, Felix Salmon writes, "[John Taylor and Glenn Hubbard], I think, would be dreadful: you really don't want your Treasury to be a political hack." A pseudonymous commentator then says:

"Is Felix really calling the creator of the Taylor rule a political hack? He’s more accomplished as an academic than anyone else mentioned in this post – arguably more accomplished as an academic than all of them put together..."

In economics, one can both continually spout lies and nonsense in the public sphere and be a very successful academic.

Noah Smith, just starting an academic career, on the other hand, characterizes the knavish Greg Mankiw as "grumpy". One needs a wide-range of euphemisms to talk about (some) supposedly leading economists.

How can economics be reformed so one would have some default reason to give economists any credibility? (Obviously, I think some economists are worth listening to.)

Sunday, May 20, 2012

I have been reporting someresultsfrom a bifurcation analysis of a formalization of Kaldor's 1940 model of the business cycle. Figures 1 and 2 illustrate the appearance of a business cycle with saddle-point stability in the Kaldor model. Suppose orbits like this arose in the dynamical system governing the solar system. Then the planets might form out of a nebular cloud. And the planets would whirl around their orbits for, maybe, millions of millenia. But then the planets will move away from their orbits, as the solar system falls apart.

Figure 2: National Output in The Business Cycle

By the way, my evidence for the existence of a limit cycle with saddle-point stability consists of graphical representations like these. I have not yet been able to find a sequence of (presumably 62) points that exactly repeat. Each of these points along such a limit cycle would have a corresponding stable and unstable set. And the possibility arises of these stable and unstable sets intertwining in a complicated fashion away from the limit cycle. The title of Agliari et al.'s paper refers to such homoclinic tangles of the stable and unstable sets of points along a limit cycle with saddle point stability. The title is not referring to a homoclinic bifurcation of a limit point at the origin, albeit they point out that bifurcation also.

Wednesday, May 16, 2012

Lars Syll has recently posted about the lack of intellectual engagement of mainstream economists with the later work of Nicholas Georgescu-Roegen. (I rely on Google Translate.) Here his a quote from an article of which Georgescu-Roegen did not think highly:

"If it is very easy to substitute other factors for natural resources, then there is in principle 'no problem.' The world can, in effect, get along without natural resources, so exhaustion is just an event, not a catastrophe." -- Robert M. Solow (1974)

Not all passages in that article are equally absurd. Who would object to the following:

"There is a limiting case, of course, in which demand goes asymptotically to zero as the price rises to infinity, and the resource is exhausted only asymptotically. But it is neither believable nor important." -- Robert M. Solow (1974)

I think the above is consistent with Solow's later view of new growth theory. Much of such work is about the behavior of models when parameters are just so. If the parameters are shifted just a bit off the knife-edge, the model does not exhibit the behavior being emphasized.

I find Georgescu-Roegen intriguing, but maybe too advanced for me. As far as the economic analysis of finite stocks of a natural resource, I also like Paul Davidson's deployment of Keynes' concept of user cost for such analysis.

I have previously noted Georgescu-Roegen's severe criticism of Brown and Robinson's 1972 paper. I now provide a link below to that paper so you can consider yourself whether or not it is just idle mathematics.

Update: Lars Syll's now has a translation of his post, "Nicholas Georgescu-Roegen and the Nobel Prize in economics".

Thursday, May 03, 2012

I have been presenting someresults from an analysis of formalizations of Kaldor's 1940 model of the business cycle. This post illustrates some possible behaviors qualitatively similar to those already reported in the literature.

Figures 2, 3, and 4 display some orbits in the (normalized) state space of the Kaldor model, with variations in one parameter determining variations in the topology of these particular phase portraits. In each figure, a movement to the right along the x axis corresponds to an increase in the value of the economy's stock of capital. A movement upward along the y axis corresponds to an increase in the national income. The propensity to save is higher for each figure in the series, but the propensity to save is always small enough that three fixed points exist for the model. In all cases, the middle fixed point has the (in) stability of a saddle point.

Figure 2: Kaldor's Model without a Business Cycle

Figure 3: A Homoclinic Bifurcation in Kaldor's Model

Figure 4: A Business Cycle in Kaldor's Model

A saddle point is such that a ball starting in the direction of the horse's head or tail rolls downward to the center. The bright yellow orbit in each of the three figures represents such a trajectory. The yellow line is known as the stable set of the corresponding fixed point. A ball would have to be balanced just so to achieve such a trajectory on an actual saddle. A ball perturbed from the center of the saddle would tend to roll downward to either side of the horse. The light blue (cyan) orbit in Figures 2 and 4 represent such a trajectory, called the unstable set of the corresponding fixed point.

A bifurcation analysis identifies qualitative changes in the phase portraits for a dynamical system with variations in the system parameters. Several bifurcations exist between Figures 2 and 3, and, I think, two bifurcations arise between Figures 3 and 4. The stable and the unstable sets of the fixed point at the origin, in some sense, have switched roles in the illustrated bifurcations. In Figure 2, the unstable set shown flows from the origin to the other two fixed points. In Figure 4, the stable set flows backwards in time from the origin to the other two fixed points. Of course, some other global behavior is an important difference among these figures. For example, a business cycle does not exist in Figure 2, while Figures 3 and 4 both display a stable business cycle. In the language of dynamical systems, this business cycle is known as a (stable) limit cycle.

The stable and the unstable sets of the origin correspond in Figure 3. Such correspondence of these sets for a given fixed point (or, say, limit cycle) is known as a homoclinic bifurcation. Homoclinic bifurcations are global phenomena and cannot be identified by a merely local stability analysis of the given fixed point. Can you see why one might draw an analogy between a homoclinic bifurcation and the M. C. Escher etching I choose to head this post with?